"ill-tempered person," 1896, earlier "state of irritable glumness" (1890, in expressions such as to have a grouch on), U.S. college student slang, of uncertain origin, possibly from grutching "complaint, grumbling" (see grutch).
The Grouch, on the other Hand, gave a correct Imitation of a Bear with a Sore Toe. His Conversation was largely made up of Grunts. He carried a Facial Expression that frightened little Children in Street Cars and took all the Starch out of sentimental Young Ladies. He seemed perpetually to carry the Hoof-Marks of a horrible Nightmare. [George Ade, "People You Know," 1902]
The verb is 1916, from the noun. Related: Grouched; grouching. Grouch bag "purse for carrying money secretly" (1908), probably so called for keeping the cash hidden from compatriots; it is the source of the nickname of U.S. comedian Julius "Groucho" Marx (1890-1977), who supposedly carried his money to poker games in one.